About curvature, conformal metrics and warped products

dc.creatorDobarro, Fernando
dc.creatorUnal, Bulent
dc.date2007-04-04
dc.date.accessioned2026-07-07T10:55:22Z
dc.date.available2026-07-07T10:55:22Z
dc.descriptionWe consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 μ}g_B \oplus w^2 g_F$, where $c, w \colon B \to (0,\infty)$ are smooth functions and $μ$ is a real parameter. We obtain suitable expressions for the Ricci tensor and scalar curvature of such products that allow us to establish results about the existence of Einstein or constant scalar curvature structures in these categories. If $(B,g_B)$ is Riemannian, the latter question involves nonlinear elliptic partial differential equations with concave-convex nonlinearities and singular partial differential equations of the Lichnerowicz-York type among others.
dc.description32 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0704.0595
dc.identifierhttp://arxiv.org/abs/0704.0595
dc.identifierJ.Phys.A40:13907-13930,2007
dc.identifierdoi:10.1088/1751-8113/40/46/006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186060
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject53C21,53C25,53C50
dc.titleAbout curvature, conformal metrics and warped products
dc.typetext

Files

Collections